Valve operable in response to engagement of different engagement members

1. A valve assembly for use in a subterranean well, the valve assembly comprising:

a valve that controls flow through a passage extending longitudinally through the valve assembly; and

an engagement device including at least first and second engagement members,

wherein the valve closes in response to:

displacement of the valve assembly in a first longitudinal direction,

engagement between the first engagement member and a first internal profile of an outer tubular string, and

continued displacement of the valve relative to the first engagement member in the first longitudinal direction, and

wherein the valve opens in response to:

displacement of the valve assembly in a second longitudinal direction,

engagement between the second engagement member and the first or a second internal profile, and

continued displacement of the valve relative to the second engagement member in the second longitudinal direction.

2. The valve assembly of claim 1 , wherein the first and second engagement members are longitudinally separated from each other on the engagement device.

3. The valve assembly of claim 1 , wherein the engagement device is reciprocably disposed relative to the valve.

4. The valve assembly of claim 1 , wherein the engagement device is secured to a mandrel that displaces with the engagement device, and wherein the mandrel displaces relative to a closure member of the valve.

5. The valve assembly of claim 1 , wherein the first engagement member disengages from the first internal profile only when the valve is closed.

6. The valve assembly of claim 1 , wherein the valve opens in response to displacement of the valve assembly in the second longitudinal direction and engagement between the second engagement member and the second internal profile.

7. The valve assembly of claim 1 , wherein the second engagement member is longitudinally displaceable relative to the first engagement member.

8. The valve assembly of claim 1 , wherein a biasing device urges the first and second engagement members in opposing directions.

9. A system for use in a subterranean well, the system comprising;

a tubular string having at least one internal profile; and

a valve assembly reciprocably disposed in the tubular string, wherein the valve assembly comprises a valve that controls flow through a passage extending longitudinally through the valve assembly, and wherein the valve is configured to be actuated between open and closed configurations by longitudinal displacement of the valve assembly within the tubular string, whereby an engagement member engages the internal profile and ceases displacement relative to the internal profile, followed by continued longitudinal displacement of the valve assembly relative to the internal profile.

10. The system of claim 9 , wherein the valve assembly is actuated to the closed configuration in response to displacement of the valve assembly in a first longitudinal direction, and wherein the valve assembly is actuated to the open configuration in response to displacement of the valve assembly in a second longitudinal direction.

11. The system of claim 9 , wherein the valve assembly includes first and second engagement members connected to an inner mandrel.

12. The system of claim 11 , wherein the first and second engagement members are longitudinally separated from each other on the valve assembly.

13. The system of claim 11 , wherein the inner mandrel is reciprocably disposed relative to the valve of the valve assembly.

14. The system of claim 11 , wherein the first engagement member engages a first internal profile in response to displacement of the valve assembly in a first longitudinal direction, and wherein the second engagement member engages a second internal profile in response to displacement of the valve assembly in a second longitudinal direction.

15. A method for use in a subterranean well, the method comprising:

displacing a service string in first and second opposite longitudinal directions within a completion assembly by manipulating an end of the service string at a surface of the well, the service string including a valve assembly that selectively restricts flow through a longitudinal flow passage of the service string;

opening the valve assembly by displacing the valve assembly in the first longitudinal direction, wherein the opening comprises ceasing displacement of a first engagement member of the valve assembly in response to engagement between the first engagement member and a first internal profile in the completion assembly; and

closing the valve assembly by displacing the valve assembly in the second longitudinal direction, wherein the closing comprises ceasing displacement of a second engagement member of the valve assembly in response to engagement between the second engagement member and the first or a second internal profile in the completion assembly, and

wherein the opening further comprises radially outwardly extending the second engagement member.

16. The method of claim 15 , wherein the first and second engagement members are longitudinally spaced apart from each other on the valve assembly.

17. The method of claim 15 , wherein the first and second engagement members are connected to an inner mandrel that reciprocably displaces relative to a valve of the valve assembly.